The maximum value of the function f(x,y) = x² + 2y² – x in the region x? + y? < 1

Q: The area of the region bounded by y = v9 – x² , the x-axis and the line y=x in the first quadrant…

A: The area between the curves y=9-x2, y=x, x=0 :The area between curves is the area between a curve fx…

Q: Find absolute extreme values of f(x,y) = 2xy² over the region R that is above the x-axis and bounded…

A: Given that f(x,y)=2xy2.

Q: Find the maximum value of s = xy + yz + xz where x + y + z = 6.

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Q: y = 2 – x2 ; y =-x

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Q: The area of the region bounded by y = v9-x² , the x-axis and the line y3x in the first quadrant is:

A: The area of the region is calculated by the double integration, and to solve double integration we…

Q: Consider the region bounded above by f(x)=−x2+9x+7 and below by g(x)=8x+5. Find the area, in square…

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Q: Find b such that the line y = b divides the region bounded by the graphs of the y = 9 − |x| and y =…

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Q: Sketch the region in the xy-plane defined by the inequalities x - 2y2 ≥ 0,   1 - x -| y| ≥ 0, and…

A: Now the graph is,

Q: 2. Find the area of the region bounded by the curve y = x^3 − 2x^2 − 5 x + 6, the x-axis, and the…

A: Given: y=x3-2x2-5x+6 For finding area of region bounded by given curve with x-axis and the lines…

Q: Find the absolute maximum of f(x,y) = 6x²y² + 4y2 + 4x2 bounded by y = x, y = 0 and x = 2. %3D

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Q: Consider the region bounded by g(x)=7x−6 and f(x)=x2+19x+14. Find the area, in square units, between…

A: The given two curves that bounds a region is,

Q: R is the region bounded by y = 4 – x2 and the x-axis and it is revolved about y = 4.

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Q: The region bounded by y = 3x – x² and y = -x %3D

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Q: Find the number k > 1 such that the region bounded by the curves y = 1, y = x-2, and x = k k has…

A: Given curves are y=1 and y=x-2 and interval is x=1 to x=k

Q: The region R is bounded by y 4 %3D and y = x +3. -

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Q: f(x) = x^2 − 3x + 2 and the line g(x) = x − 1 over the interval [0,2] .

A: Being bounded means that one can enclose the whole graph between two horizontal lines.

Q: Find a such that the line x = a divides the region bounded by the graphs of the equations into two…

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Q: The area of the region bounded above by yx+7. bounded below by vey2, bounded from the left by x2 and…

A: The given region is as shown. Now, It is bounded above by y=x+7 and below by y=x2. So, the upper…

Q: The area of the region bounded by the curve y= e", the x-axis,'the y-axis, and the line x 2 is equal…

A: We have to find the area of the region bounded by the curve y=e2x , the x-axis, y-axis and the line…

Q: Find the absolute maximum and minimum values for f (x, y) = 5 sin(x) + 9cos(y) on the rectangle R…

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Q: The area of the region between the curve y x'-6x+ 8 and the x-axis & x=0; x= 3 is given by -6x+8)kke…

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Q: Volumes Find the volume of the described solid of revolution or state that it does not exist.

A: Given function is f(x)=1x lnx and the interval is [2, ∞).

Q: The area of the region bounded by the curve y= x3−3x2−x+3 and y=0 is

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Q: The region is bounded by y = x³, y = 2x + 4 and y = -1. Then Area region = [ f(x) dx + √ [*g(x) dx…

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Q: The area of the region bounded by the curves y =x and y = 20–x² is попe 4.4 O 4= " |20–x²-x| dr -4.4…

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Q: Find the area of the region bounded by the parabola f(x) = 16-x^2 and the lines  x=0 and x = 4 and…

A: Givenf(x) = 16-x2lines x=0, x=4 and x-axis(y=20)

Q: find the absolute maximum and minimum values of ƒ on the region R. ƒ(x, y) = x2 - y2 - 2x + 4y R:…

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Q: 4. Find the absolute maximum and minimum of the function on the given closed bounded region. y…

A: Given function is fx,y=ex2-4x-2y+y2 Closed region is x=0,y=0 and x+y=3 The objective is to find the…

Q: The region bounded by f(x) = (x + 1)-³ and the x-axis on the interval [0, ∞) is revolved about the…

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Q: Determine the absolute maximum and minimum values of f(x, y) = 2+4x–2x²+4y-y² on the region R…

A: The region bounded by the x-axis,y=3x and x=2 is:

Q: Find a such that the line x = a divides the region bounded by the graphs of the equations into two…

A: Given, y2=4-xx=0

Q: y = Vx - x² - re sen /x

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Q: Find a such that the line x = a divides the region bounded by the graphs of the equations into two…

A: Given,    y = x,  y = 4  and  x = 0 So the region bounded by these curves is given by shaded region…

Q: Areas of regions Find the area of the following regions.

A: Given that, y=10x2-2x-24

Q: The area of the region bounded by the 2 curves f(x) = x² + 1 and g(x) = 2x + 1 is best described by:…

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Q: Find b such that the line y = b divides the region bounded by the graphs of the two equations into…

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Q: R is the region bounded by y = x², y = 4x - x² and the line x = and it is revolved about y = 0.

A: Given regions are, y=x2y=4x-x2y=0 Now, using Washer method by the formula, V=π∫abR2-r2dx

Q: If f(x, y) is continuous, then it must have an absolute maximum in the region x? + y² < 1. True…

A: Given: f(x,y) is continuous Region R is an open circle centre at origin and radius 1 ie x2+y2 &lt; 1…

Q: The region bounded by the curves y=1-x^3. ,y=e^x.  And the line y=3

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Q: The region is bounded by the curve y = 6x – x² and y = x² – 2x – 10

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Q: Find the value of k between –1 and 2 such that the area of the region bounded by the lines y = -x, y…

A: we know that the area of a triangle with vertices A(x1, y1), B(x2, y2) and C(x3, y3) is given by…

Q: Find the maximum and minimum of f(x, y) = xy-x+y-1 on the region: x^2+y^2 &lt;= 4.

A: A scalar function f(x,y) is a rule that is used to associate a number, or quantity with a particular…

Q: 2) Find the absolute maximum and minimum for function F(x,y)= 4x³-2x²y+y² on the region R bounded by…

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Q: The area of the region bounded by the curves f(x)=x²+1 and g(x)=2x+1 is best described by: a. ² [(2x…

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Q: find the absolute maximum and minimum valuesof ƒ on the region R. ƒ(x, y) = x2 + xy + y2 - 3x + 3y…

A: Let us consider the given function, f(x, y)=x2+xy+y2-3x+3y .....(1)  The triangular region cut from…

Q: on Find the absolute minimum and maximum of the function f(x, y) = 2x¹ - xy² + 2y² the region 0≤x≤…

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Q: The region is bounded by y = x³, y = 2x + 4 and y = -1. Then Arearegion = [*^f(x) dx + [²8(x) x +…

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